The noun resolution has a few related meanings having to do with being firmly determined about something. If you lack determination, you'll never fulfill your New Year's resolutions.
Resolution is the noun form of the verb resolve, which comes from Latin resolvere, "to loosen, undo, settle." We can still see this meaning in resolution, in the sense of "an explanation" or "a solution"; when a problem, conflict or mystery reaches its resolution, it has been "undone," so to speak. Another common meaning is "determination, resolve": "Jose approached the task with resolution." A related sense is "a decision to do something": "My resolution is to go to the gym three times a week."